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8.2 Inscribing shapes in circles

c Step 1 Start by drawing a Step 2 Make a mark at
circle with radius 4 cm. any point on the
4 cm
Mark the centre of the circumference of
circle with a small dot. the circle.

Step 3 Check that the Step 4 Move your
compasses are still set compasses to the
to 4 cm (radius of the first arc (made
circle). Put the point on in the previous
the mark you have just step) and draw a
made and draw an arc second arc on the
on the circumference of circumference.
the circle.
Step 5 Repeat step 4 until Step 6 oin the original
J
you have drawn five mark to the
arcs. second arc, then
this arc to the
fourth, then this
arc to the original
mark, to form
d Repeat steps 1–5 of part c. an equilateral
triangle.
J
Step 6 oin the original mark to the first
arc, then continue to join the arcs,
in order. Join the last arc to the first
mark, to form a regular hexagon.

) Exercise 8.2

1 For each part of this question, start by drawing a circle with radius 5 cm.
Use a straight edge and compasses to construct an inscribed:
a square b regular octagon
c equilateral triangle d regular hexagon.
2 The diagram shows a square inscribed in a circle of radius 6 cm. x
a Draw an accurate copy of the diagram.
b Measure the length of the side of the square, which is marked x in 6 cm
the diagram.
Write your measurement to the nearest millimetre.
c Copy and complete the workings below to calculate the area of the
shaded region in the diagram. Use π = 3.14.
Area of circle: π × r = π × 6 2
2
= cm 2
Area of square: x × x = ×
= cm 2
Shaded area: area of circle − area of square = −
= cm 2

8 Constructions and Pythagoras’ theorem 79